hysteresis analysis of strawbale masonr1

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BUILDING RESEARCH JOURNAL VOLUME 55, 2007 NUMBER 3 Hysteresis analysis of prestressed brick frame with strawbale masonry-infill subjected to seismic loads A A Adedeji Department of Civil Engineering, University of Ilorin, Ilorin, Nigeria Email: [email protected] Pseudo-dynamic earthquake response tests, of a one quarter (¼) scale model three storeys prestressed bricks frames stiffened with cement plastered strawbale masonry, was conducted. The structure was idealized as plane frames. The analysis utilised the hysteresis models for members’ models as time- independent. The force-displacement relationship of the members’ models was evaluated by the approximate method on the basis of the material properties and structural geometry. A hysteretic model was investigated with straw bale infill panel to determine the hysteretic parameters, stiffness deterioration and strength degradation due to seismic loadings. The average design thickness, for the cement-plastered strawbale stiffens the prestressed burnt-brick frame, was obtained. Keywords: seismic; masonry-infill; strawbale, finite element; degradation, prestressed brick

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Page 1: Hysteresis Analysis of Strawbale Masonr1

BUILDING RESEARCH JOURNALVOLUME 55, 2007 NUMBER 3

Hysteresis analysis of prestressed brick frame with strawbale masonry-infill subjected to seismic loads

A A AdedejiDepartment of Civil Engineering, University of Ilorin, Ilorin, Nigeria

Email: [email protected]

Pseudo-dynamic earthquake response tests, of a one quarter (¼) scale model three storeys prestressed bricks frames stiffened with cement plastered strawbale masonry, was conducted. The structure was idealized as plane frames. The analysis utilised the hysteresis models for members’ models as time-independent. The force-displacement relationship of the members’ models was evaluated by the approximate method on the basis of the material properties and structural geometry. A hysteretic model was investigated with straw bale infill panel to determine the hysteretic parameters, stiffness deterioration and strength degradation due to seismic loadings. The average design thickness, for the cement-plastered strawbale stiffens the prestressed burnt-brick frame, was obtained.

Keywords: seismic; masonry-infill; strawbale, finite element; degradation, prestressed brick

1. Introduction

A number of past studies (Klinger and Bertero 1978; Bertero and Brokken 1983; Mander and Nair 1994) focused on evaluating the experimental behavior of masonry infilled frames to obtain formulations of limit strength and equivalent stiffness. A more rigorous analysis of structures with masonry infilled frames requires an analytical model of the force – deformation response of masonry infill. While a number of finite element models have been developed to predict the response of infilled frames (Dhanasekar and Page 1986. Mosalam 1996, Malnotra 2002), such micro modeling is time-consuming for analysis of large structures. Alternatively, a macro model allows treatment of the entire infill panel as a single unit.

Saneinejad and Hobbs (1995) developed a method based on the equivalent diagonal strut approach for the analysis and design of frames with masonry infill walls subjected to in-

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plane forces. The UBC required that the shear walls acting independently of the ductile moment-resisting portions of the frame shall resist total required seismic forces. It is also required that design force distributions along elevations of the structure for both axial-flexural and shear design shall be the same. It has been observed from the research carried out by Ahmet et al (1984) the UBC later claim could be realized by shear design based on calculation that demands that consider actual flexural capacity of the walls. The actual contribution of the edge members (columns and beams) panel RC/ prestressed concrete should be considered in evaluating available shear strength. Therefore the study has recommended that in designing and evaluating of strength of wall, cross section should be considered rather than the assumption of edge column acting as axially loaded members that should resist all vertical members from the loads acting on the wall.

Based on the aforementioned claim, the objective of this paper was to provide the average design thickness for the cement-plastered strawbale stiffens the prestressed burnt-brick frame. Data on strength and deformation of the structure are the input for the analytical models. The plastered strawbale wall was connected to the frame with mortar (1:6 cement-sand mix) to constitute a simple support. This is shown in Fig. 1. The project also covers the hysteresis analysis of the straw bale wall infill in terms of stiffness deterioration and strength degradation in order to determine the response of the infill due to dynamic loading.

150

Prestressed brick beam B Tendon

A Bar tie A’ Joint mortar

Strawbale wall B’VERTICAL SECTION SECTION B-B’

Prestressed brick column

HORIZONTAL SECTION A-A’

Fig. 1.Infill-frame interaction

A A Adedeji

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2. Modelling of Structural Members

2.1 Frame: Beam and Column Members

A one-dimensional model was used for beam and column in this paper. The beam or column member was idealized as a perfectly idealized elastic massless line element with two nonlinear rotational springs at he two ends. The model could have two rigid zones outside the rotational spring.

2.2 Analytical Model of strawbale Infill

Shear walls can be idealized as (a) an equivalent column taking flexural and shear deformation into account, (b) a braced frame in which the shear deformation is represented by deformation of diagonal elements, where the structural deformation is by the deformation of vertical element and (c) short line represent along the height with each short segment with hysteretic characteristics. These models have advantages and disadvantages. In most cases the horizontal boundary beams are assumed to be rigid.

The proposed analytical model assumes that the contribution of the straw bale wall infill panel (Fig. 3a) to the response of the infilled frame can be modeled by replacing the panel by a system of two diagonal straw bale wall compression struts (Fig 3(b)). Since the tensile strength of masonry is negligible, the individual straw bale strut is considered to be in effective in tension. However, the combination of both diagonal struts provides a lateral load resisting mechanism for the opposite lateral directions of loading. The lateral force-deformation relationship for the structural straw bale infill panel is assumed to be a smooth curve bounded by a bilinear strength envelope until the yield force Vy and then on a post yield degraded stiffness until the maximum force Vm is reached (Fig 3). The corresponding lateral displacement values are denoted as Vy and Um respectively.

2. 2.1 Strawbale Wall as Infill Panel

The use of strawbale infill for the construction of a building in place of conventional materials is its cheapness, availability and flexibility in terms of workability and strength.

151

Rigid zone Elastic element Non-linear rotational Springs

Fig. 2. One-dimensional model for beam and column

Hysteresis analysis of prestressed brick frame with strawbale masonry-infill subjected to seismic loads

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Though the individual straw bale strut is considered to be in effective in tension, yet strawbale masonry has a high tensile strength.

The load resisting mechanism of infill frames is idealized as a combination of moment resisting frame system formed by the frame and a pin-jointed system formed by the strawbale. However, because of the absence of a realistic, yet simple analytical model, the plastered straw bales as infill panels might be neglected in the non-linear analysis of building structures. Such an assumption may lead to substantial inaccuracy in predicting the lateral stiffness, strength, and ductility of the structure.

Saneinejad and Hobbs (1995) developed a method based on the equivalent diagonal strut approach for the analysis and design of steel or concrete frames with masonry infill walls subjected to in-plane forces. The method takes into account the elastoplastic behaviour of infilled frames considering the limited ductility of infill materials. The formulation provides only extreme or boundary values for design purposes. In the case of straw bale panel, the aspect ratio, shear stresses at the interface between the infill and frame, together with the frame strength were accounted for and the formulation expresses the boundary values for design purposes.

3. Equivalent Strut ModelThe description, in brief, of the formulations for predicting the lateral strength and stiffness

parameters of the strawbale infill-panel is presented in this section.Considering the straw-bale infilled frame as shown in Fig 3 (a) and Fig.4 , the maximum lateral

force Vm and corresponding displacement Um in the infill straw bale panel are expressed as,

Vm+ (Vm

-) < Ad f¢ m cos q < Vtl ¢ < 0.83tl ¢ (1) (1-0.45 tan q) cos q cosq

Um+ (Um

-) = emLd (2) Cosq

where t = thickness of the infill panel: l¢ = lateral dimension of the wall panel : f’m = masonry strength, em = corresponding strain, q = inclination of the diagonal strut to the horizontal; V =

152

Fig..3 Strength envelopes for masonry infill

K0

Kpy Um- Uy

-

Uy+ Um

+

Vy-

Vm-

V

Vm

Vy

Ko

A A Adedeji

Hysteresis analysis of prestressed brick frame with strawbale masonry-infill subjected to seismic loads

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V = shear strength (average of 0.347 N/mm2), of straw bale wall; and Ad , Ld = area and length of the equivalent diagonal struts respectively calculated as,

Ad = (1- c)c t h¢ sc + b t l¢ tb < 0.5t h ¢ f a / fc (3) ¦c ¦c cos q and

Ld = Ö ((1 - c )2 h ¢2 + L¢2 (4)

153

(a) Straw bale wall infill frame sub assemblage

Straw bale infill panel

h

Frame

1

(b) Straw bale wall infill panel

Fig. 4. Wall equivalent diagonal strut

(1 -

b)

b h¢

h

¢

q

A A Adedeji

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Where the quantities c, b, = ratio of wall length (breadth) to the contact length between the infill and frame respectively, sc, tb, compressive and shear stress of wall respectively, ¦a, and ¦c, compressive strength for frame and wall respectively. Saneinejad and Hobbs (1995) proposed the formulations of the equivalent strut model. The initial stiffness Ko of the infill straw bale wall panel is estimated using the following formula.

The lateral yield force Vy and corresponding displacement Uy of the infill panel may be calculated from geometry as;

where = ratio of post yield stiffness (Kpy) to initial (Ko) stiffness (See Fig. 2)

4. Seismic Load Analysis

4.1 Time-independent smooth hysteresis model

A smooth hysteretic model proposed by Beber and wen (1981) is used for the structural straw bale masonry infill panel. The model, which was developed based on the Bouc–Wen model for hysteresis behaviour furnishes a smooth hysteresis force-displacement relationship between force V and displacement U is,

Vi = Vy [mi + (1 - ) Zi] (8)

Where m = ductility calculated as Ui/Uy, subscript i = instantaneous values, subscript y = yield values, and Z = hysteretic component determined by solving the following differential equation by Reinhorn (1995) as;

dZi = [aeff – êZi ên [b sgn (dmi Z) + g]] d m (9)

where signum function sgn( x) = 1 for x > 0 and = -1 for x < 0; aeff , b , and g = constants that control the shape of the generated hysteretic loops (Assumed values a eff = 1, and b = g = 0.5. At x = 0, the effect of cyclic loading is neglected) and n controls the rate of transition from the elastic to yield state.

4.2. Stiffness decayThe yielding system in general is the loss of stiffness due to deformation beyond yield

point. The stiffness decay is incorporated directly in the hysteretic model by including the control parameter h in equation (9) for hysteretic parameter Z in which h is obtained by pivotal deterioration method (Valles et al, 1996).

dZi =[ aeff - ½Zi½n[b sgn(dmiZ)+g] ] dmi/ h (10)

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Hysteresis analysis of prestressed brick frame with strawbale masonry-infill subjected to seismic loads

Page 7: Hysteresis Analysis of Strawbale Masonr1

for mI > 1.0where Sk = multiplier for Vs to define the pivot for stiffness deterioration. A default value of Sk is taken to be 5.

4.3 Strength degradation

Degrading systems such as straw bale wall infill panels will also exhibit loss of strength in the inelastic range. The strength deterioration is modeled by reducing the yield force Vy from the original value Vy

o at each step k,Vy

k = Vyk (1 – DI) (12)

in which DI = cumulative damage parameter dependent on the maximum attained ductility, mmax, and the cumulative energy dissipated ( Valles 1996).

where mmax, mc = maximum and monotonic ductility capacity and parameters Sp1 and Sp2

control the rate of deterioration for maximum and monotonic ductility respectively. The damage index was derived from fatigue consideration (Reinhorn et al, 1995).

4.4. Cracking slip model

Opening and closing of masonry cracks resulting in the pinching of hysteresis loops is a commonly observed phenomenon in masonry structural systems subjected to cyclic loading. The concept of slip lock element proposed by Baber and Noori (1984) was adopted in this study to formulate a hysteretic model. A slip–lock element is incorporated in series so that displacement ductility m = m1 + m2, with the smooth degrading element m1. The displacement ductility component m2 due to the slip-lock element is defined by the following relationship:

dm2 = a f(Z) dZ (14)

in which a = (As(m2-1), at As is the parameter for varying the slip length due to crack opening in the panel and m2 = ductility attained at the load reversal prior to the current unloading or reloading cycle.) is the slip length and assumed to be a function of the attained ductility while the function f(Z) is defined as:

¦(Z) = exp((Z -Z1 )2) (15) Zs

2

at -1< Z, and Z1 < 1

where Z1 = value of Z at which f(Z) reaches its maximum; Zs = range of Z , about Z = Z1 , in which the slip occurs. Derived from Eq.(9), (14), and (15), the hysteretic parameter Z will satisfy the following differential equation (Reinhorn. 1995).

155

A A Adedeji

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5. Experimental Tests

5.1 Test Structure and properties of materials The test structure represented a three-storey one-bay (span prestressed concrete ductile moment resisting frame filled with straw bale masonry), built at a scale of ¼. The overall geometry of the test structure is depicted in Fig. 5. Analytical example was carried out for a full scale version of the test structure and all pertinent quantities were scaled using the length factor of 0.25. Each tested structure consists of strawbale wall (made of 127x78x61 mm 3 unit size; elephant grass bale plastered with 1: 6 cement-sand mix ratio; average density of 2200 kg/m3; 12% absorption and moisture content of 3.61. Its average compressive and flexural strengths are 2.83 and 1.56 N/mm2) respectively) whose principal plane was parallel with the direction of the input motion. The prestressed bricks frame (column-beam) was constructed of concrete with grade of 40 N/mm2 and cable of diametre 12mm.

Design gravity loads comprised of 70 kN (self weight and live load). Seismic design effects were determined using modal spectral analysis. The design spectral ordinates were set so that the first-mode shear base was equal to the design base shear required by the UBC 1982 for a ductile moment-resisting space frame. Also, the response spectrum was selected to reflect soil condition that superseded by a layer of sandy soil. Earthquake design actions were

156

Column 0.75

Beam 0.75MortarWall 0.75

SECTION A-A’

0.075 0.05 1.26 0.05 0.075 1.26 0.075 0.05 0.05 0.075

PLAN All dimensions in m

Fig. 5. Test structure

Hysteresis analysis of prestressed brick frame with strawbale masonry-infill subjected to seismic loads

Page 9: Hysteresis Analysis of Strawbale Masonr1

determined with a three dimensional elastic analysis model based on the cross section of columns and beams. The three dimensional structure was idealized as a pseudo-three-dimensional model in which only the planar modes of the main structural systems (walls and frames) were considered. The considerations of stiffness and strength of frame elements perpendicular to the plane of the transverse walls and frames were not considered. Perfect base fixity of the frames was assumed. Horizontal floor level responses have been recoded in lateral and main direction.

At 3.2 m/s2, the structure did not increase its response. The maximum base shear of 129 kN is obtained at the roof displacement of 12.3 mm.

5.2 Test and Instrumentation

Tests included earthquake simulation of varying intensity and followed by low amplitude free vibration tests. The simulations were conducted by applying unilateral horizontal base motions parallel to the direction frame. The input signals to the shaking table modeled accelerated history for uniaxial tests are as indicated in Table 1 with a total of four earthquake records. These values were used as input ground motions in the dynamic analysis. These values are notations used for individual ground motion, the components of earthquake motion record, peak ground acceleration (aeff) in terms acceleration due to gravity (g), peak ground velocity (vg), significant duration of the accelerogram (tSD) and the normalized characteristics intensity (In).

Table 1 Characteristics of selected input earthquake ground motionGround motion

Notation Peak ground acceleration(aeff)

Peak ground velocity (vg) m/s

Significant duration (tSD), s

normalized characteristics intensity (In)

El Centro ELCENT 0.35g 0.34 24 2.66Haruka-oki HARU 0.42g 0.46 6 2.12Silmar SYLM 0.84g 0.61 47 1.71Hacinohe HACH 0.23g 0.34 28 1.52

6. Typical Analysis Example

6.1. Sections properties

Beam and column sectional area are shown in Fig. 6 . Second moment of area (Ib) = 2.278 x 10-3 m4(Ic) = 6.75 x 10 -4 mm4 respectively. The straw bale wall is measured acting as diagonal members of the frame in this analysis. It acts as a stiffening element and the area and length of the equivalent diagonals are as calculated below, Ld = 6681.6mm and area of equivalent diagonal strut (Fig. 6)., Ad = 14235.0 mm2.

157

C

A

B

D E

F

G

H

3

@ 3

m =

9 m

6 m

(a) Fig..6. A three-storey building

300 mm

450 mm

(c) Column section

300 mm

450 mm

( b) Beam section

AdA A Adedeji

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6.2. Earthquake analysis and loading

For the absorption and dissipation of the energy through its motion, the frame of the building must be sufficiently ductile. For calculating ductility and other parameters it is assumed that the tests were entered to the ductile mode. Fig 7 shows the calculated shear loading during seismic excitation. It is assumed that during a strong ground motion the inertial of a building results in a horizontal shear force at the base and proportional to the weight of the building and the imposed ground motion, so that:

VD = Cs M g (23)

And

where VD = total dynamic base shear, M = total mass of the building and its contents (kg), g = acceleration due to gravity, Cs = seismic coefficient, aeff = dependent effective peak acceleration , S = seismic response factor, R = factor related to ductility of structure or force reduction factor, and In= normalized characteristics intensity. A good example of the seismic record characteristics is given by Moroni et al (1996) from 1985 Chilean earthquake. Assumed for the prestressed brick frame is the ductility factor R = 5 (braced frame, with effective peak acceleration aeff = 0.1 – 0.2g, seismic response factor S = 2 and the intensity factor = 1, so that the seismic coefficient Cs = 0.04. The total design base shear is 143.3kN.

158

A

B

C

DE

F

G

H

3 @

3.0

m =

9.0

m

6.0 m

17.61 kN/m

21.63 kN/m

21.63 kN/m

Fig.7. Equivalent Lateral Loads

Horizontal load during seismic excitation

Horizontal load during seismic excitation

Horizontal level during seismic excitation

Hysteresis analysis of prestressed brick frame with strawbale masonry-infill subjected to seismic loads

Page 11: Hysteresis Analysis of Strawbale Masonr1

6.3 Analysis of bare frame

The basic concept of this method is based on the fact hat the inertia of a building result in a horizontal shearing force at the base proportional to the total weight of the building and to the imposed ground motion during a period of strong ground motion.

6.4. Database

The three-storey building shown in Fig 8 has been analysed by the equivalent lateral force procedure. Weight at each storey level = 21.63 x 6 = 129. 8 kN, Weight at the roof = 17.61 x 6 = 105.66 kN and the total mass Mtotal = 36.526 kg. Therefore the total design base shear = 256.4 kN. The lateral forces on the building are distributed over its height accordingly. The sum of the lateral forces is equal to the total base shear. The lateral forces on the building frame are shown in Table 2 and Fig. 8.

Table 2 Seismic forces on Building frameStorey level Equivalent

lateral force (kN)

Equivalent lateral shear force (kN)

Roof21

41.4571.65143.3

41.45113.10256.40

Total dynamic base shear 256.4

159Fig.8. Members moments and shear forces

430.16 kN

300.36 kN

158.5

36.21

158.6158.6

36.21

158.5

A A Adedeji

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The maximum lateral force and corresponding displacement in the infill straw bale panel are as follows:

At q = 32o and using equations (1) to (7), Vm+ (Vm

-) = 14486.4N = 14486N, while the corresponding displacement Um

+ (Um-) = 23.6mm. The initial stiffness Ko of the infill panel is

estimated Ko =1227.63N/mm, the lateral yield force and displacement of the infill panel is 14193 .4 N and Uy +(Uy

-) = 11. 7mm. Using different straw bale thickness, the result of the analysis for the stiffness deterioration and shear decay are shown in Table 3.

Table 3 Stiffness deterioration and shear decay of straw bale infill for the thickness (t) = 300m

Instantaneous value, (i)

Displacement Ui (mm)

Lateral force Vi (N)

Shear decay (Vm - Vi (N)

Initial stiffness Ko (N/mm)

123456

11.700011.818311.916911.998812.382523.6000

14340.114365.214386.214403.614485.114486.4

146.3121.20100.282.801.300.00

25.00920.51116.81713.8010.2090.000

CASE II, t = 275mm, Ad = 13048.8mm2, Vm = 13279.2N, Um = 23.6mm, KO=1125. 4N/mm, Vy = 13145.1 N, Uy = 11.7mm.The result of the analysis is shown in Table.2

Table 2 Stiffness Deterioration and shear Decay of straw bale infill for the thickness (t) = 275mm

Instantaneous Displacement Lateral force Shear decay Vm Stiffness initial

160

Hysteresis analysis of prestressed brick frame with strawbale masonry-infill subjected to seismic loads

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value (Test No) i

Ui (mm) Vi (N) - Vi (N) Ko (N/mm)

123456

11.700011.817911.916211.997912.380323.6000

13145.113168.113187.213203.113277.613279.2

134.10111.1092.0076.101.600.00

22.92318.80215.44112.6860.2590.000

At the instantaneous value 6, other cases (CASES III and IV) with varying wall thicknesses (t) are:

CASE III at t = 250mm, Ad = 11862.53mm2, Vm = 12071.9N, Um = 23.6mm, KO=1023. 05N/mm, and Vy = 11949.9 N, Uy = 11.7mm .CASE IV, t = 200mm, Ad = 10961.62mm2, Vm = 11155.2N, Um = 23.6mm, KO=945. 36N/mm and Vy = 11042. 5N, Uy = 11.7mm.

6.5. Deflection check Maximum deflection of masonry wall is 24 mm. This value is greater than 23.7mm that was obtained in the analysis. Thus, the maximum deflection of the straw bale infill is less than the maximum allowed for masonry walls with the same dimensions (6.000 x 3.500 m).

It is beyond the scope of this paper to verify the accuracy of the spectra response on the basis of the shake table runs and because of the compressed time-scale of the laboratory study (at Department of Civil Engineering, University of Ilorin), it would not be correct to make such correlation. However, it is worthy to examine how well the actual peak response agreed with those determined from the linear response from actual base motion. The results are shown in Table 4.

Table 4. Observed and measured response maxima for base isolated motionResponse Table

accelerationPeak acceleration

Spectral acceleration

Base shearkN

Total weight of the structure kN

Base momentkNm

Roof displacement

Mm

Observed (prototype)

1.07 0.58 0.59 129 210 95.8 12.3

Calculated - 0.1 - 143 365.62 158.6 23.6

6.6. Dynamic response results At calculated Z =1, the stiffness decay is incorporated in the hysteretic model by including the control parameter h for the hysteretic parameter (hi > 1.0). The default value of Sk = 5 is recommended. The results of iteration of dynamic response characteristics from the analysis are as shown in the Tables 5 and 6 for 200 and 250 only.

161

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Table 5 Dynamic response characteristics of straw bale infill thickness (t) = 200mmDisplacement (Ui)

Ductility (mi)

Control parameter (hi)

Hysteretic Component (dZi)

Lateral force (Vi), N

Shear decay (Vm –Vi), N

11.7 1.0 1 1 11042.5 112.7011.8205 1.0103 0.9983 1.0017 11.062.22 92.9811.9210 1.0189 0.9969 1.0031 11078.66 76.5412.0045 1.0260 0.9957 1.0043 11092.32 62.8812.0737 1.0319 0.9948 1.0053 11103.64 51.5612.1311 1.0368 0.9940 1.0061 11113 42.2012.1782 1.0409 0.9933 1.0067 11120.72 34.4812.2171 1.0442 0.9928 1.0073 11127.09 28.1112.2491 1.0469 0.9923 1.0077 11132.33 22.8712.2754 1.0492 0.9920 1.0081 11136.64 18.5612.971 1.0510 0.9917 1.0084 11140.13 15.0312.3148 1.0526 0.9914 1.0087 11143.08 12.12

Table 6 Dynamic response characteristics of straw bale infill thickness (t) = 250mmDisplacement (Ui)

Ductility (mi)

Control parameter (hi)

Hysteretic Component (dZi)

Lateral force (Vi), N

Shear decay (Vm-Vi), N

11.7 1 1 1 11949.9 12211.8224 1.0105 0.9983 1.0017 11971.58 100.3211.9245 1.0192 0.9968 1.0032 11989.65 82.2512.0094 1.0264 0.9957 1.0044 12004.67 67.2312.0797 1.0325 0.9947 1.0054 12017.12 54.7812.1378 1.0374 0.9939 1.0062 12027.41 44.4912.1858 1.0415 0.9932 1.0069 12035.9 36.0012.2253 1.0449 0.9927 1.0074 12042.9 29.0012.2578 1.0477 0.9922 1.0079 12048.66 23.2412.2846 1.0500 0.9918 1.0082 12053.4 18.5112.3066 1.0518 0.9915 1.0086 12057.29 14.6212.3246 1.0534 0.9913 1.0088 12060.48 11.46

Other dynamic response results for t = 275 and 300 are not shown here, but are represented in the graphical forms. The strength deterioration is modeled by reducing the yield force Vy

from Vyo at each step k.

7. Results and Discussion

It was observed, from the result of the analysis, that the maximum lateral force the straw bale infill can be subjected to increases with the thickness of the infill panel. For thickness of 200mm,Vm = 11155.2N; for t = 250mm,Vm = 12071.9N; for t = 275mm, Vm =13279.2N and for t = 300mm, Vm = 14486N. Also, the stiffness and strength (hysteretic properties) of the straw bale wall infill decreases after the yield force. The yield force (Vy) being 14193.4N for t=300mm; 13145.1N for t = 275mm; 11949.9N for t = 250mm and 11042.5N for t = 200mm. The maximum deflection of the infill was obtained to be 23.7mm, which was less than the maximum 24mm specified for masonry infill walls. Also, it was found out that the hysteretic parameters deteriorate at a rate proportional to the thickness of the infill panel

As a result of the seismic loads, the force-displacement relationships for the loading cases, stiffness decay and the wall strength degradation are shown in Figs. (9), (10) and (11)

162

A A Adedeji

Hysteresis analysis of prestressed brick frame with strawbale masonry-infill subjected to seismic loads

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respectively.. The hysteresis-energy dissipation due to seismic load was reduced detriment to damage of the structure.

It was also observed that the structure shear decay increases with decrease in ductility of the wall infill.

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8. Concluding Remarks

The use of straw bale wall as an infill panel for the proposed hysteretic model can compete effectively with other conventional materials, such as earthwall (Adedeji, 2002), since its maximum deflection Um, is less than that specified for masonry walls.

Though a perfect base fixity of the frames was assumed, the structure did not increase its response at 3.2 m/s2. The maximum base shear of 129 kN is obtained at the roof displacement of 12.3 mm. these are far less values than the analysis results.

The computed force-deformation response can be used to assess the overall structural damage and its distribution to a sufficient degree of accuracy.

The structural materials characteristics were nominal values and may be different from the prescribed values. Such characteristics of materials for further analysis should be based on the confined and unconfined prestressed concrete.

9. ReferencesAdedeji, A.A. (2001). Hysteresis analysis of framed structures stiffened with earth wall infill

subjected to seismic Impact, Conference Proc. SUSI–2002, UK. Adedeji, A.A. (2003). Analytical approach to framed structures stiffened with earth wall

infill subjected to seismic loads, LAUJET Journal, 1(1). Ahmet, E., Aktan, M., Vitelmo, V and Bertero, E., (1984), Seismic response of R/C frame-

wall structures, Journal of Structural Engineering, 111(8), 1803 – 1821. Berber, T. T. and Noori, M. N. (1985). Random Vibration of degrading pinching system,

Journal of Engineering Mech, ASCE 11(8): 1011-1026.Bertero, V.V., and Broken, S. (1983). Infills in Seismic resistant building. Journal of

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10. Symbolsaeff = Dependent effective peak accelerationA b = Sectional area of beam Ac = Sectional area of columnAd = Area of equivalent diagonal strut. As = Parameter varying the slip length due to crack opening in the panelCs = Seismic coefficient DI = Cumulative damage parameterfb = Brick compressive strength.f ¢m = Characteristic strength of straw bale wall.Gk = Dead load g = Acceleration due to gravity h ¢ = Vertical dimension of in fill panel. Ib = Moment of inertia of bean Ic = Moment of inertia of column Iw = Second moment of area of equivalent diagonal strut In = normalized characteristics intensityi = Instantaneous value.Ko = Initial stiffness.L ¢ = Lateral dimension of infill panel.Ld = Length of the equivalent diagonal strut.M = Total mass of the building and its contents

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n = Transitional rates.Qk = Live load R = Ductility factor of the structure {r} = Displacement vector S = Seismic response factor Sp1 ,Sp2 = Control the rate of deterioration for maximum and monotonic ductility respectivelySk = Default value.t =Thickness of infill panel. tSD = significant duration of the accelerogram)U = Ultimate load Um = Corresponding maximum displacement.Uy = Corresponding yield displacement.V = Base shear VD = Total dynamic base shearVm = Maximum lateral force.Vy = Lateral yield force.Vb = Total dynamic base shear vg = peak ground velocity Z = Hysteresis component.b = Bond strength of straw bale [wall].β = Constant that control the shape of the generated hysteresis ε¢m = Corresponding strain.q = Inclination of diagonal strut mi = Ductility h = Control parameter.sC = Basic compressive strength of straw bale tb = Shear stress of plain straw bale wall.txy = Tangential stress

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